arch-chroot does more than create a chroot: it also creates a PID namespace.
unshare --fork --pid chroot "$chrootdir" "$@"
As the name suggests, a PID namespace has its own set of process IDs, distinct from the rest of the system. This means that processes inside the namespace can't see the processes outside the namespace (and in particular can't kill or trace them), and processes outside the namespace¹ see them with different PIDs.
For more information on namespaces, read my summary here and the LWN series by Michael Kerrisk, especially Part 3: PID namespaces and Part 4: more on PID namespaces, as well as the earlier article by Pavel Emelyanov and Kir Kolyshkin. how to find out namespace of a particular process? and Reliable way to jail child processes using `nsenter:` may also be of interest.
If you want to do things to a process running in a namespace from outside, you can use the
nsenter utility; see Is there a command to switch to into an existing namespace?. You can also use the
nsenter Python package. Or you can arrange to do these operations from inside the namespace (this may or may not be a good solution depending on your architecture and security requirements); it's easier to access something in a chroot from the outside (just prefix the right directory path) than in a PID namespace.
Note that PID namespaces and chroots are independent. If you chroot to the same directory independently, that doesn't let you reach the same PID namespace. If you run
arch-chroot twice on the same directory, you end up working in the same directory, but in two different PID namespaces.
¹ More precisely, in an ancestor namespace. (Namespaces have a tree structure where children are confined within the parent.)
echo $$work as expected?